Question: Simplify the following expression: $a = \dfrac{-12r^2}{-108r^2 - 84r}$ You can assume $r \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-12r^2 = - (2\cdot2\cdot3 \cdot r \cdot r)$ The denominator can be factored: $-108r^2 - 84r = - (2\cdot2\cdot3\cdot3\cdot3 \cdot r \cdot r) - (2\cdot2\cdot3\cdot7 \cdot r)$ The greatest common factor of all the terms is $12r$ Factoring out $12r$ gives us: $a = \dfrac{(12r)(-r)}{(12r)(-9r - 7)}$ Dividing both the numerator and denominator by $12r$ gives: $a = \dfrac{-r}{-9r - 7}$